Follow these steps to update your controller wirelessly and to support the Xbox One Stereo Headset Adapter:

Sign in to Xbox Live on your Xbox One console and install the latest system update if prompted to do so.

If you have a stereo headset adapter, plug it into the bottom of your controller so it can also get updates.

If you’re using a stereo headset adapter, plug in a headset (a headset must be plugged in so the adapter will turn on).

Press the Menu button.

Select Settings.

Select Devices & accessories.

Select the controller you want to update.

Select Update, and then select Continue.

When the update is complete, you can update additional controllers. If they can only be updated via USB, see Update via USB. Otherwise, select the Update another button on the screen after the first update is complete, and then follow the steps.

Xbox One Controller Joystick Drift Fix video

The stick drift is usually caused by plastic dust (from the thumbstick wearing against the shell of the controller) gumming up the analog mechanism that tracks the position of the thumbstick. I get it occasionally on my left thumbstick, and I fix it by prizing off the plastic piece on side of the controller grip, exposing the space between the circuit board and the shell, and blasting some canned air at the mechanism to clean it.